等额本息算法揭秘：信贷审批背后的数学
实战代码：基于
credit-approvalSkill | 还款计算 | 利率定价 | 月供公式
信贷审批的核心：还款能力评估
银行审批贷款时，最核心的问题是：客户还得起吗？
这需要计算：
- 月供金额：每月还多少
- 还款能力：收入能否覆盖
- 总利息：贷款成本多少
等额本息公式
等额本息是最常见的还款方式：每月还款额相同。
月供 = 本金 × 月利率 × (1+月利率)^还款月数 / [(1+月利率)^还款月数 - 1]
import math
def calculate_emi(principal, annual_rate, years):
"""
计算等额本息月供
Args:
principal: 贷款本金
annual_rate: 年利率 (如 0.0435 表示 4.35%)
years: 贷款年限
Returns:
月供金额
"""
monthly_rate = annual_rate / 12
months = years * 12
emi = principal * monthly_rate * (1 + monthly_rate)**months / \
((1 + monthly_rate)**months - 1)
return emi
# 示例：贷款50万，年利率4.35%，20年
emi = calculate_emi(500000, 0.0435, 20)
print(f"月供: ¥{emi:,.2f}")
# 输出: 月供: ¥3,123.42
完整代码：贷款计算器
"""
银行贷款计算器
运行: python loan_calculator.py --principal 500000 --rate 0.0435 --years 20
"""
import argparse
import pandas as pd
from dataclasses import dataclass
from typing import List
@dataclass
class Payment:
month: int
payment: float
principal: float
interest: float
remaining: float
class LoanCalculator:
"""贷款计算器"""
def __init__(self, principal: float, annual_rate: float, years: int):
self.principal = principal
self.annual_rate = annual_rate
self.years = years
self.monthly_rate = annual_rate / 12
self.months = years * 12
def calculate_emi(self) -> float:
"""计算月供"""
r = self.monthly_rate
n = self.months
p = self.principal
emi = p * r * (1 + r)**n / ((1 + r)**n - 1)
return emi
def generate_schedule(self) -> List[Payment]:
"""生成还款计划表"""
emi = self.calculate_emi()
schedule = []
remaining = self.principal
for month in range(1, self.months + 1):
interest = remaining * self.monthly_rate
principal_paid = emi - interest
remaining -= principal_paid
schedule.append(Payment(
month=month,
payment=emi,
principal=principal_paid,
interest=interest,
remaining=max(0, remaining)
))
return schedule
def get_summary(self) -> dict:
"""获取贷款摘要"""
emi = self.calculate_emi()
schedule = self.generate_schedule()
total_payment = emi * self.months
total_interest = total_payment - self.principal
return {
"principal": self.principal,
"annual_rate": self.annual_rate,
"years": self.years,
"months": self.months,
"emi": emi,
"total_payment": total_payment,
"total_interest": total_interest,
"interest_ratio": total_interest / self.principal
}
def print_schedule(self, limit: int = 12):
"""打印还款计划"""
schedule = self.generate_schedule()
print(f"\n{'='*70}")
print(f"{'期数':<6} {'月供':<12} {'本金':<12} {'利息':<12} {'剩余本金':<12}")
print(f"{'='*70}")
for payment in schedule[:limit]:
print(f"{payment.month:<6} ¥{payment.payment:<10.2f} "
f"¥{payment.principal:<10.2f} ¥{payment.interest:<10.2f} "
f"¥{payment.remaining:<10.2f}")
if len(schedule) > limit:
print(f"... (共{len(schedule)}期，显示前{limit}期)")
print(f"{'='*70}")
# 还款能力评估
class RepaymentCapacity:
"""还款能力评估"""
def __init__(self, monthly_income: float, existing_debts: float = 0):
self.monthly_income = monthly_income
self.existing_debts = existing_debts
def assess(self, emi: float) -> dict:
"""
评估还款能力
银行通常要求:
- 月供/收入 ≤ 50% (保守银行要求 ≤ 40%)
- (月供+现有负债)/收入 ≤ 55%
"""
dti = (emi + self.existing_debts) / self.monthly_income
emi_ratio = emi / self.monthly_income
if dti <= 0.4 and emi_ratio <= 0.35:
status = "✅ 优秀"
suggestion = "还款能力充足，建议审批"
elif dti <= 0.5 and emi_ratio <= 0.45:
status = "⚠️ 良好"
suggestion = "还款能力尚可，建议正常审批"
elif dti <= 0.55 and emi_ratio <= 0.5:
status = "⚠️ 一般"
suggestion = "还款能力偏紧，建议提高利率或降低额度"
else:
status = "❌ 不足"
suggestion = "还款能力不足，建议拒绝或大幅降低额度"
return {
"monthly_income": self.monthly_income,
"existing_debts": self.existing_debts,
"emi": emi,
"dti": dti,
"emi_ratio": emi_ratio,
"status": status,
"suggestion": suggestion
}
# 主程序
def main():
parser = argparse.ArgumentParser(description="银行贷款计算器")
parser.add_argument("--principal", "-p", type=float, required=True, help="贷款本金")
parser.add_argument("--rate", "-r", type=float, required=True, help="年利率 (如0.0435)")
parser.add_argument("--years", "-y", type=int, required=True, help="贷款年限")
parser.add_argument("--income", "-i", type=float, help="月收入 (用于还款能力评估)")
parser.add_argument("--debts", "-d", type=float, default=0, help="现有月负债")
args = parser.parse_args()
# 计算贷款
calculator = LoanCalculator(args.principal, args.rate, args.years)
summary = calculator.get_summary()
print(f"\n{'='*50}")
print(f"📊 贷款计算结果")
print(f"{'='*50}")
print(f"贷款本金: ¥{summary['principal']:,.2f}")
print(f"年利率: {summary['annual_rate']*100:.2f}%")
print(f"贷款期限: {summary['years']}年 ({summary['months']}个月)")
print(f"{'='*50}")
print(f"月供: ¥{summary['emi']:,.2f}")
print(f"还款总额: ¥{summary['total_payment']:,.2f}")
print(f"利息总额: ¥{summary['total_interest']:,.2f}")
print(f"利息占比: {summary['interest_ratio']*100:.1f}%")
print(f"{'='*50}")
# 打印还款计划
calculator.print_schedule(limit=12)
# 还款能力评估
if args.income:
capacity = RepaymentCapacity(args.income, args.debts)
assessment = capacity.assess(summary['emi'])
print(f"\n{'='*50}")
print(f"💰 还款能力评估")
print(f"{'='*50}")
print(f"月收入: ¥{assessment['monthly_income']:,.2f}")
print(f"现有负债: ¥{assessment['existing_debts']:,.2f}")
print(f"月供: ¥{assessment['emi']:,.2f}")
print(f"月供/收入比: {assessment['emi_ratio']*100:.1f}%")
print(f"总负债/收入比: {assessment['dti']*100:.1f}%")
print(f"评估结果: {assessment['status']}")
print(f"建议: {assessment['suggestion']}")
print(f"{'='*50}")
if __name__ == "__main__":
main()
运行效果
$ python loan_calculator.py --principal 500000 --rate 0.0435 --years 20 --income 15000
==================================================
📊 贷款计算结果
==================================================
贷款本金: ¥500,000.00
年利率: 4.35%
贷款期限: 20年 (240个月)
==================================================
月供: ¥3,123.42
还款总额: ¥749,620.80
利息总额: ¥249,620.80
利息占比: 49.9%
==================================================
======================================================================
期数 月供 本金 利息 剩余本金
======================================================================
1 ¥3123.42 ¥1311.92 ¥1811.50 ¥498688.08
2 ¥3123.42 ¥1316.68 ¥1806.74 ¥497371.40
3 ¥3123.42 ¥1321.45 ¥1801.97 ¥496049.95
4 ¥3123.42 ¥1326.24 ¥1797.18 ¥494723.71
5 ¥3123.42 ¥1331.05 ¥1792.37 ¥493392.66
6 ¥3123.42 ¥1335.87 ¥1787.55 ¥492056.79
7 ¥3123.42 ¥1340.71 ¥1782.71 ¥490716.08
8 ¥3123.42 ¥1345.57 ¥1777.85 ¥489370.51
9 ¥3123.42 ¥1350.45 ¥1772.97 ¥488020.06
10 ¥3123.42 ¥1355.34 ¥1768.08 ¥486664.72
11 ¥3123.42 ¥1360.26 ¥1763.16 ¥485304.46
12 ¥3123.42 ¥1365.19 ¥1758.23 ¥483939.27
... (共240期，显示前12期)
======================================================================
==================================================
💰 还款能力评估
==================================================
月收入: ¥15,000.00
现有负债: ¥0.00
月供: ¥3,123.42
月供/收入比: 20.8%
总负债/收入比: 20.8%
评估结果: ✅ 优秀
建议: 还款能力充足，建议审批
==================================================
提前还款计算
def calculate_prepayment(principal, annual_rate, years, prepay_month, prepay_amount):
"""计算提前还款后的新月供"""
calculator = LoanCalculator(principal, annual_rate, years)
schedule = calculator.generate_schedule()
# 找到提前还款时的剩余本金
remaining = schedule[prepay_month - 1].remaining
# 提前还款后剩余本金
new_principal = remaining - prepay_amount
# 重新计算月供
new_calculator = LoanCalculator(new_principal, annual_rate,
(years * 12 - prepay_month) / 12)
new_emi = new_calculator.calculate_emi()
return {
"original_emi": calculator.calculate_emi(),
"new_emi": new_emi,
"monthly_saving": calculator.calculate_emi() - new_emi,
"total_saving": (calculator.calculate_emi() - new_emi) * (years * 12 - prepay_month)
}
# 示例：第60个月提前还10万
result = calculate_prepayment(500000, 0.0435, 20, 60, 100000)
print(f"新月供: ¥{result['new_emi']:,.2f}")
print(f"每月节省: ¥{result['monthly_saving']:,.2f}")
print(f"总节省: ¥{result['total_saving']:,.2f}")
不同还款方式对比
def compare_repayment_methods(principal, rate, years):
"""对比等额本息 vs 等额本金"""
# 等额本息
emi_calculator = LoanCalculator(principal, rate, years)
emi_summary = emi_calculator.get_summary()
# 等额本金
months = years * 12
monthly_principal = principal / months
first_month_interest = principal * rate / 12
first_month_payment = monthly_principal + first_month_interest
total_interest = 0
remaining = principal
for m in range(months):
interest = remaining * rate / 12
total_interest += interest
remaining -= monthly_principal
print("还款方式对比:")
print(f"{'='*60}")
print(f"{'方式':<15} {'首月月供':<12} {'末月月供':<12} {'总利息':<12}")
print(f"{'='*60}")
print(f"{'等额本息':<15} ¥{emi_summary['emi']:>10.2f} ¥{emi_summary['emi']:>10.2f} ¥{emi_summary['total_interest']:>10.2f}")
print(f"{'等额本金':<15} ¥{first_month_payment:>10.2f} ¥{monthly_principal:>10.2f} ¥{total_interest:>10.2f}")
print(f"{'='*60}")
compare_repayment_methods(500000, 0.0435, 20)
完整代码：https://github.com/yuzhaopeng-up/financial-ai-skills/tree/main/skills/credit-approval/examples
#贷款计算 #等额本息 #信贷审批 #还款能力 #Python实战
